The use of electrical measurements in prior art downhole applications, such as logging while drilling (LWD), measurement while drilling (MWD), and wireline logging applications is well known. Such techniques are commonly utilized to determine a subterranean formation resistivity, which, along with formation porosity measurements, may be used to indicate the presence of hydrocarbons in the formation. For example, it is known in the art that porous formations having a high electrical resistivity often contain hydrocarbons, such as crude oil, while porous formations having a low electrical resistivity are often water saturated. It will be appreciated that the terms resistivity and conductivity are often used interchangeably in the art. Those of ordinary skill in the art will readily recognize that these quantities are reciprocals and that one may be converted to the other via simple mathematical calculations. Mention of one or the other herein is for convenience of description, and is not intended in a limiting sense.
Directional resistivity measurements are also commonly utilized to provide information about remote geological features (e.g., remote beds and boundary layers) not intercepted by the measurement tool. In geosteering applications, directional resistivity measurements may be utilized in making steering decisions for subsequent drilling of the borehole. In order to make correct steering decisions, information about the strata, such as the dip and strike angles of the boundaries of the oil-bearing layer, and the relative location and orientation of the drill string in the strata is generally required. Directional resistivity measurements, and in particular borehole images derived from such measurements, are commonly utilized to estimate some or all of the above formation properties.
Downhole imaging tools are conventional in wireline applications. Such wireline tools typically create images by sending large quantities of azimuthally sensitive logging data uphole via a high-speed data link (e.g., a cable). Further, such wireline tools are typically stabilized and centralized in the borehole and include multiple (often times six or more) sensors extending outward from the tool into contact (or near contact) with the borehole wall. It will be appreciated by those of ordinary skill in the art that such wireline arrangements are not suitable for typical LWD applications. In particular, communication bandwidth with the surface would typically be insufficient during LWD operations to carry large amounts of image-related data. Further, LWD tools are generally not centralized or stabilized during operation and thus require more rugged sensor arrangements.
Several attempts have been made to develop LWD tools and methods that may be used to provide images of various azimuthally sensitive sensor measurements related to borehole and/or formation properties. Many such attempts have made use of the rotation (turning) of the BHA (and therefore the LWD sensors) during drilling of the borehole. For example, Holenka et al., in U.S. Pat. No. 5,473,158, discloses a method in which sensor data (e.g., neutron count rate) is grouped by quadrant about the circumference of the borehole. Likewise, Edwards et al., in U.S. Pat. No. 6,307,199, Kurkoski, in U.S. Pat. No. 6,584,837, and Spross, in U.S. Pat. No. 6,619,395, disclose similar methods. For example, Kurkoski discloses a method for obtaining a binned azimuthal density of the formation. In the disclosed method, gamma ray counts are grouped into azimuthal sectors (bins) typically covering 45 degrees in azimuth. Accordingly, a first sector may include data collected when the sensor is positioned at an azimuth in the range from about 0 to about 45 degrees, a second sector may include data collected when the sensor is positioned at an azimuth in the range from about 45 to about 90 degrees, and so on.
As described above, one problem with implementing LWD imaging techniques is that imaging techniques, in general, typically require large data storage and/or data transmission capacity. Due to the limited conventional communication bandwidth between a BRA and the surface, as well as limited conventional downhole data storage capacity, the sensor data used to form the images must typically undergo significant quantity reduction. Conventional techniques as described above accomplish such data quantity reduction via “binning” sensor data into a plurality of azimuthal sectors (also referred to bins or azimuthal bins). While binning techniques have been utilized in commercial LWD applications, both real-time and memory LWD images are often coarse or grainy (and therefore of poor quality) and in need of improvement. For example, when the number of bins is small (e.g., quadrants or octants), conventional binning strongly distorts the high-frequency components of the data which results in aliasing. When the number of bins is large (e.g., 32 or more), there may not be enough data points for each bin to generate a stable (low noise) output. Conventional binning techniques may therefore not be an optimal approach to forming LWD images.
More recently, commonly assigned U.S. Pat. No. 7,027,926 to Haugland discloses a technique in which LWD sensor data is convolved with a one-dimensional window function. This approach advantageously provides for superior image resolution and noise rejection as compared with the previously described binning techniques and in particular reduces the aforementioned aliasing problem. Commonly assigned, co-pending U.S. Patent Publication 2009/0030616 (now U.S. Pat. No. 7,558,675) to Sugiura describes an image constructing technique in which sensor data is probabilistically distributed in either one or two dimensions (e.g., azimuth and measured depth). This approach also advantageously provides for superior image resolution and noise rejection as compared to prior art binning techniques. Moreover, it further conserves logging sensor data (i.e., the data is not over or under sampled during the probabilistic distribution) such that integration of the distributed data may also provide a non-azimuthally sensitive logging measurement. Notwithstanding the improvements disclosed in the '926 patent and the '043 publication, there remains room for further improvement of LWD imaging methods, in particular for directional resistivity imaging.